A singer-songwriter wishes to compose a melody. each note in the melody must be one of the 1010 notes in her vocal range. how many different sequences of 33 notes are possible?

I assume the question was for a sequence of 3 notes out of the possible 10. If not, use the number 1010 and 33 with the same plan.

There would be 720 different sequences.

To  find the number of ways, just multiply the number of possibilities for each note. 

There are 10 for the first, then 9 for the second, and finally 8.
10 x 9 x 8 = 720